1,846 research outputs found
Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental findings and applications
Inferring information from a set of acquired data is the main objective of
any signal processing (SP) method. In particular, the common problem of
estimating the value of a vector of parameters from a set of noisy measurements
is at the core of a plethora of scientific and technological advances in the
last decades; for example, wireless communications, radar and sonar,
biomedicine, image processing, and seismology, just to name a few. Developing
an estimation algorithm often begins by assuming a statistical model for the
measured data, i.e. a probability density function (pdf) which if correct,
fully characterizes the behaviour of the collected data/measurements.
Experience with real data, however, often exposes the limitations of any
assumed data model since modelling errors at some level are always present.
Consequently, the true data model and the model assumed to derive the
estimation algorithm could differ. When this happens, the model is said to be
mismatched or misspecified. Therefore, understanding the possible performance
loss or regret that an estimation algorithm could experience under model
misspecification is of crucial importance for any SP practitioner. Further,
understanding the limits on the performance of any estimator subject to model
misspecification is of practical interest. Motivated by the widespread and
practical need to assess the performance of a mismatched estimator, the goal of
this paper is to help to bring attention to the main theoretical findings on
estimation theory, and in particular on lower bounds under model
misspecification, that have been published in the statistical and econometrical
literature in the last fifty years. Secondly, some applications are discussed
to illustrate the broad range of areas and problems to which this framework
extends, and consequently the numerous opportunities available for SP
researchers.Comment: To appear in the IEEE Signal Processing Magazin
Estimation of longitudinal stability and control derivatives for an icing research aircraft from flight data
The results of applying a modified stepwise regression algorithm and a maximum likelihood algorithm to flight data from a twin-engine commuter-class icing research aircraft are presented. The results are in the form of body-axis stability and control derivatives related to the short-period, longitudinal motion of the aircraft. Data were analyzed for the baseline (uniced) and for the airplane with an artificial glaze ice shape attached to the leading edge of the horizontal tail. The results are discussed as to the accuracy of the derivative estimates and the difference between the derivative values found for the baseline and the iced airplane. Additional comparisons were made between the maximum likelihood results and the modified stepwise regression results with causes for any discrepancies postulated
Cramer-Rao bounds in the estimation of time of arrival in fading channels
This paper computes the Cramer-Rao bounds for the time of arrival estimation in a multipath Rice and Rayleigh fading scenario, conditioned to the previous estimation of a set of propagation channels, since these channel estimates (correlation between received signal and the pilot sequence) are sufficient statistics in the estimation of delays. Furthermore, channel estimation is a constitutive block in receivers, so we can take advantage of this information to improve timing estimation by using time and space diversity. The received signal is modeled as coming from a scattering environment that disperses the signal both in space and time. Spatial scattering is modeled with a Gaussian distribution and temporal dispersion as an exponential random variable. The impact of the sampling rate, the roll-off factor, the spatial and temporal correlation among channel estimates, the number of channel estimates, and the use of multiple sensors in the antenna at the receiver is studied and related to the mobile subscriber positioning issue. To our knowledge, this model is the only one of its kind as a result of the relationship between the space-time diversity and the accuracy of the timing estimation.Peer ReviewedPostprint (published version
Quantum interferometry with three-dimensional geometry
Quantum interferometry uses quantum resources to improve phase estimation
with respect to classical methods. Here we propose and theoretically
investigate a new quantum interferometric scheme based on three-dimensional
waveguide devices. These can be implemented by femtosecond laser waveguide
writing, recently adopted for quantum applications. In particular, multiarm
interferometers include "tritter" and "quarter" as basic elements,
corresponding to the generalization of a beam splitter to a 3- and 4-port
splitter, respectively. By injecting Fock states in the input ports of such
interferometers, fringe patterns characterized by nonclassical visibilities are
expected. This enables outperforming the quantum Fisher information obtained
with classical fields in phase estimation. We also discuss the possibility of
achieving the simultaneous estimation of more than one optical phase. This
approach is expected to open new perspectives to quantum enhanced sensing and
metrology performed in integrated photonic.Comment: 7 pages (+4 Supplementary Information), 5 figure
Cramer-Rao bounds for nonparametric surface reconstruction from range data
technical reportThe Cramer-Rao error bound provides a fundamental limit on the expected performance of a statistical estimator. The error bound depends on the general properties of the system, but not on the specific properties of the estimator or the solution. The Cramer-Rao error bound has been applied to scalar- and vector-valued estimators and recently to parametric shape estimators. However, nonparametric, low-level surface representations are an important important tool in 3D reconstruction, and are particularly useful for representing complex scenes with arbitrary shapes and topologies. This paper presents a generalization of the Cramer-Rao error bound to nonparametric shape estimators. Specifically, we derive the error bound for the full 3D reconstruction of scenes from multiple range images
On the Performance Limits of Pilot-Based Estimation of Bandlimited Frequency-Selective Communication Channels
In this paper the problem of assessing bounds on the accuracy of pilot-based
estimation of a bandlimited frequency selective communication channel is
tackled. Mean square error is taken as a figure of merit in channel estimation
and a tapped-delay line model is adopted to represent a continuous time channel
via a finite number of unknown parameters. This allows to derive some
properties of optimal waveforms for channel sounding and closed form Cramer-Rao
bounds
Range Precision of LADAR Systems
A key application of Laser Detection and Ranging (LADAR) systems is measurement of range to a target. Many modern LADAR systems are capable of transmitting laser pulses that are less than a few nanoseconds in duration. These short-duration pulses provide excellent range precision. However, randomness in the detected laser signals places limits on the precision. The goal of this dissertation is to quantify the range precision limits of LADAR systems. The randomness in the time between photon arrivals, which is called shot noise, is discussed in depth. System-dependent noise sources such as dark current and detector gain variation are considered. The effect of scene-dependent parameters including background light, target obscuration, and target orientation is also discussed. Finally, noise mitigation strategies such as pulse averaging and gain equalization are described and tested on simulated and real LADAR data
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